Ali has been given a list of
6
bands and asked to place a vote. His vote must have the names of his favorite and second favorite bands from the list. How many different votes are possible?
if a is the favorite, there are five choices for b. Yet instead of a, there are six choices for first, and five for second.
number votes: 6*5=30
To find the total number of different votes possible, we need to consider that Ali has to choose his favorite band and his second favorite band.
Since Ali has a list of 6 bands to choose from, he has 6 options for his favorite band. After choosing his favorite band, he now has 5 bands left to choose from for his second favorite band.
Therefore, the total number of different votes possible is the product of the number of options for his favorite band and the number of options for his second favorite band:
Total number of different votes = Number of options for favorite band × Number of options for second favorite band
Total number of different votes = 6 × 5 = 30
So there are 30 different votes possible for Ali.